Cubature Methods and Applications
Cubature Methods and Applications
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培养方法及应用
DOI：
10.1007/978-3-319-00413-6_4
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
C. Nee
中科院分区：
文献类型：
--
作者：
D. Crisan;K. Manolarakis;C. Nee
我们介绍了一类新的数值方法，用于近似随机微分方程解的分布。这些方法的收敛结果基于 Kusuoka 和 Stroock 在扩散半群的非 Hormader 约束下建立的某些尖锐梯度界限。这些讲座涵盖了这些界限和其他一些后续改进。除了描述新一类方法和相应的收敛结果之外，我们还包括这些方法在向后随机微分方程数值求解中的应用。众所周知，后向随机微分方程在金融衍生品定价中发挥着核心作用。
We present an introduction to a new class of numerical methods for approximating distributions of solutions of stochastic differential equations. The convergence results for these methods are based on certain sharp gradient bounds established by Kusuoka and Stroock under non-Hormader constraints on diffusion semigroups. These bounds and some other subsequent refinements are covered in these lectures. In addition to the description of the new class of methods and the corresponding convergence results, we include an application of these methods to the numerical solution of backward stochastic differential equations. As it is well-known, backward stochastic differential equations play a central role in pricing financial derivatives.